Yeah, when SSBB first came out it bricked countless systems, including mine (2 weeks after I bought the game). Since it is a dual-layer disk, it works the Wii harder and caused many systems to break. Just tell Nintendo that you just bought SSBB and your system broke while playing it. They'll ask you to send in the game and the system and they will do it all for free.

At least, they should.

I have a loophole for you.
Tell them that your Wii wont read your Super Smash Bros Brawl disc. They'll tell you to send the Wii in for a free cleaning. When they test it, they'll see that its not reading the disc still and you can say it was playing other games fine. The likely nature, due to their good customer service, is that they'll fix it for free, thinking they broke it somehow.

Edit - ah I see someone beat me to the idea =p

That solution will work (SSSB). They caught a lot of heat due to Brawl problems and will bend over backwards to fix them.

An example of how good the service is..... A few weeks ago my daughter had a dead spot on her DS touch screen (in warranty, the touch screen would not recognize the pen on the lower left part of the screen). I sent it in for repair, Ninty paid for shipping both ways. The DS also had a hairline crack on the hinge, and a small scratch on the screen (which is not covered by the warranty) and they fixed that without my asking and without charge. Total time from my call to it's return: 8 days.